MATH 290
Covers 4.1-4.6
The topics include:
- Recall the definition of a vector space, the 10 axioms.
- Verifying a set with two given operations is a vector space.
- Writing a vector as a linear combination of other given vectors.
- Determining if a given subset is a subspace.
- Giving a geometric description of a subspace.
- Definition of the span of a given set of vectors.
- Geometric description of the span of a given set of vectors.
- Determining if a vector is in the span of a given set.
- Determining if a given set of vectors is spanning.
- Notions of linear dependence and linear independence of vectors.
- Testing linear dependence and linear independence of vectors.
- Notions of basis and dimension.
- Writing the standard basis for well-known vector spaces.
- Determining if a given set of vectors is a basis.
- Finding a basis and the dimension of a vector space or a subspace.
- Computing the rank and nullity of a matrix.
- Recall the Rank-Nullity Theorem.
- Finding a basis and the dimension of a subspace spanned by a given set of
vectors using RREF of matrices.
